Anybody please help me in how to begin with this cryptarithm. I tried to find for 0,1,5,6,9 but none of them are clearly recognizable..
o u i * o u i
l i a r
m l m a
t h u s
m s i e u r
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$\begingroup$ o,u,i,l,a,r,m,t,h,s,e: 11 symbols... really??? $\endgroup$– Oleg567Jul 12, 2013 at 9:24
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1$\begingroup$ I'd start by looking at $u$. It isn't often that the tens digit of $x$ and $x^2$ are the same. $\endgroup$– Gerry MyersonJul 12, 2013 at 9:27
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$\begingroup$ Try 783*783 (1-st sieve: as Gerry Myerson said, 2-st sieve: oui*u = mlma, m on 1-st and 3-rd place, m>t>0). Here a=h=4. $\endgroup$– Oleg567Jul 12, 2013 at 10:29
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$\begingroup$ Just a note: not all cryptarithms are in base 10. $\endgroup$– TrurlJul 12, 2013 at 13:36
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1 Answer
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Starting hint:
First note that there are 11 symbols in cryptarithm: o,u,i,l,a,r,m,t,h,s,e.
So, in decimal system, at least two of symbols are equal.
A). t +1 = m. $\ \ \implies \ $ thus < mlma $\ \ \implies \ $ oui*o < oui*u $\ \ \implies \ $ o < u.
B). oui*oui = msieur $\ \ \implies \ $ m $\le$ o, $\ \ $ o $\ge$ $3$.
C). So we get: $\ \ 0$ < t < m $\le$ o < u $\ \ \ \ $ ( t + 1 = m ).
D).
Applying comment of Gerry Myerson, we search "ui", such that u $\ge$ 4,
_ui * _ui = ____ur,
and get 6 possible cases:
_43 * _43 = ____49,
_63 * _63 = ____69,
_69 * _69 = ____61,
_74 * _74 = ____76,
_76 * _76 = ____76, (here i=r=6),
_83 * _83 = ____89.
E). Now we search "oui", where o $\ge$ $3$, and
oui * u = mlma.
_43: no results;
_63: no results;
_69: no results;
_74: no results;
_76: 476 * 7 = 3332;
_83: 783 * 8 = 6264.
F). There are 2 possible numbers for "oui": $476$ and $783$.
$783$ * $783$ works, but a=h=4 (because there are 11 symbols in cryptarithm: o,u,i,l,a,r,m,t,h,s,e).
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$\begingroup$ A long time spent. no reaction. I decided to continue answer. $\endgroup$– Oleg567Jul 13, 2013 at 10:31